A Statistical Theory of the Disruption of Three-Body Systems -- II: HIGH ANGULAR MOMENTUM

Abstract

The statistical theory of the disruption of three-body self-gravitating systems is refined by allowing for both energy and angular momentum conservation in the phase space description. The resulting distribution of the parameters of the remnant binary, and the velocity distribution of the escaping particle are in good agreement with the numerical experiments. I.INTRODUCTION The statistical theory of the disruption of strongly interacting, self-gravitating three-body systems is based on the assumption that the statistical properties of the final state are determined by the volume of phase space allowed by the constants of motion. In an earlier paper (Monaghan 1976, hereafter I) the analysis of the statistical theory was simplified by assuming that, for systems with small total angular momentum, the only relevant constant of motion is the total energy and, in addition, the total energy of the escaping body is sufficiently large to allow its gravitational interaction with the remnant binary to be neglected. This simplified theory predicts an eccentricity distribution for the remnant binary which is in good agreement with the low angular momentum numerical experiments (Standish 1972; Saslaw, Valtonen & Aarseth 1974). The predictions of the energy distribution of the escaping body agree only qualitatively with the experiments. The mass distribution of the escaping particle is in reasonable quantitative agreement with the numerical experiments, but it underestimates the probability of having an escaper with very small mass. In the present paper the effects of angular momentum conservation and the escaper-binary interaction are analysed. The effect of the angular momentum is the more important of the two and, for this reason, we begin the analysis by assuming the escaper-binary interaction can be ignored. The resulting phase space distribution gives a good description of the statistical properties of the binary and the escaper for both small and large angular momentum configurations. The analysis is completed by including the gravitational interaction between the binary and the escaper and establishing the way the distributions which result reduce to those neglecting the interaction. The theory contains one arbitrary parameter, a length 7?, which determines the size of the interaction region.